Eigenvectors of a Toeplitz Matrix: Discrete Version of the Prolate Spheroidal Wave Functions

Abstract

The discrete Fourier transform leads one, in a natural way, to consider the extent to which a function in $Z_N $ and its transform can both be sharply concentrated. This requires the study of a Toeplitz matrix and its eigenvalues and eigenvectors. For the case at hand this can be done successfully.